Method for detecting freezing conditions for an aircraft by supervised automatic learning

ABSTRACT

A method for detecting icing conditions for an aircraft including a measurement of the parameters of embedded systems, with the exception of probes dedicated to the detection of ice, a transformation of the measurements of the symptomatic parameters to obtain P-tuples of values of explanatory variables which explain icing conditions, a classification of the measurements by classifiers on the basis of the P-tuples of values thus obtained, the classifiers having been previously trained in a supervised manner, each classifier providing a prediction of membership in a class of icing conditions, the predictions of the various classifiers being consolidated to provide a consolidated prediction of icing conditions.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to French patent application 18 50553filed on Jan. 24, 2018, the entire disclosure of which is incorporatedby reference herein.

TECHNICAL FIELD

The disclosure herein relates generally to forecasting of meteorologicalconditions for an aircraft. It also relates to the field of supervisedlearning (supervised machine learning).

BACKGROUND

The occurrence of freezing conditions in flight constitutes a risk foraircraft. Indeed, when an aircraft encounters such conditions, it isexposed to an accumulation of ice on its surfaces which can lead to anappreciable increase in the weight of the aircraft, a loss of lift,problems actuating the control surfaces, defects in communication andoperation of the antennas, measurement errors of the anemometric probes,losses of engine thrust, these various malfunctions possibly ultimatelyleading to a loss of control of the airplane.

To alleviate these malfunctions, aircraft entitled to fly in freezingconditions are equipped with ad hoc protection systems, notably heatingsystems, integrated into the elements to be protected (airfoil, probes,engine air inlets, etc.) preventing the formation or the accumulation ofice.

The activation of these protection systems generally relies on thejudgment of the pilot after the latter has visually identified thepresence of freezing conditions. This identification necessarily beingimperfect, recourse is generally had to mechanical or optical detectionsystems to aid the pilot in their judgment. Thus, it is commonplace toequip an aircraft with probes (or sensors) mounted on the skin of theairplane and to utilize the measurements obtained to diagnose thepresence of ice. However, these detection systems do not generallytrigger the activation of the protection systems automatically. Anassessment of the measurements by the pilot is still necessary takinginto account the flight phase, the criticality of the functionsfulfilled by the elements affected by the ice and associated safetymargins, so as to avoid any untimely triggering of the protectionsystems.

Current systems for detecting freezing conditions exhibit severaldrawbacks.

Firstly, these systems are installed on the skin of the fuselage or asurface of the aircraft, which, on the one hand, makes it necessary todrill into the fuselage/the surface in question, to provide mechanicalstrengthening in proximity to the hole, to deploy electrical wiring andto install additional acquisition systems in electrical cabinets.Furthermore, the sensors/probes often protrude from the skin of thefuselage and consequently cause induced drag, thereby affecting theperformance of the aircraft.

Next, current systems for detecting freezing conditions have relativelylimited performance in the sense that they are only capable ofresponding to certain very limited conditions of ice formation. They aregenerally ineffective when dealing with detecting the formation of bigdrops of water or of crystals of large size.

An object of the disclosure herein is to propose a method for detectingfreezing conditions for an aircraft, which at least partly remedies thedrawbacks hereinabove, in particular which does not require anyadditional drilling and wiring operations, does not increases either theweight of the airplane or its aerodynamic drag, and makes it possible atone and the same time to appraise a wide range of freezing conditionsand to provide a more precise diagnosis than in the prior art.

SUMMARY

The disclosure herein relates to a method for detecting icing conditionsfor an aircraft, comprising:

-   -   measurement of parameters of systems of the aircraft with the        exception of ice-detecting external probes, the systems being        unsusceptible to degraded operation in the presence of ice and        the parameters being symptomatic of the presence of ice on the        aircraft;    -   transformation of the measurements of these parameters into        P-tuples of values of explanatory variables which explain the        icing conditions;    -   classification of the measurements by at least one classifier        previously trained in a supervised manner, the classifier        providing a prediction of membership in a class of icing        conditions.

The parameters of systems of the aircraft are advantageously chosen fromamong the lists of parameters from ATA21, ATA27, ATA28, ATA30, ATA32,ATA34, ATA36, ATA70 to ATA79.

The parameters can be selected from among temperatures, currents ofheating circuits, pressures, disparities between actuator commands andfeedbacks, kinematic, altimetric, barometric and anemometric parameters.

The transformation of the measurements of parameters into values ofexplanatory variables comprises for example the calculation of a mean,of a median, of a standard deviation, of a variance, a Fouriertransform, a low-pass or high-pass filtering, a wavelet decomposition, aspectral density calculation.

The classification step is advantageously performed by a plurality ofclassifiers, the respective predictions of these classifiers beingconsolidated, the result of the consolidation giving a prediction of thepresence/absence of ice or otherwise, or else a degree of severity ofthe icing conditions.

The classifiers preferably use classification models chosen from among adecision-tree classification model, a classification model based onlinear discriminant analysis, a classification model based on quadraticdiscriminant analysis, a classification model based on a forest ofdecision trees, a classification model using a bagging of decisiontrees, a classification model using a logistic regression, aclassification model using the method of k nearest neighbors, aclassification model using a boosting of weak classifiers.

The measurements of parameters can notably be transmitted by the craftto a ground station, the ground station performing the transformationand classification steps and then returning the result of theconsolidation to the aircraft.

The disclosure herein also relates to a method of supervised training ofthe above-defined method for predicting icing conditions, the method ofsupervised training comprising:

-   -   measurement of the parameters of systems of the aircraft during        a flight under freezing conditions;    -   transformation of the measurements of these parameters into        P-tuples of values of explanatory variables which explain the        icing conditions;    -   detection of presence of freezing conditions during the flight        by dedicated probes situated on the aircraft;    -   allocation of classes of freezing conditions to the measurements        on the basis of the conditions detected in the previous step;    -   training of a plurality of classifiers on the basis of the        explanatory variables and of the corresponding classes        allocated;    -   comparison of the prediction performance of the classifiers by        cross-validation over the set of measurements;    -   selection of at least one classifier from among the best        performing classifiers to predict the icing conditions.

Preferably, the detection of presence of freezing conditions during theflight also uses meteorological sources external to the aircraft.

The prediction performance of a classifier is for example estimated onthe basis of the mean absolute value of the prediction error or of themean square value of the prediction error or of the mean success rate ofprediction over the set of measurements.

The classification models are advantageously chosen from among adecision-tree classification model, a classification model based onlinear discriminant analysis, a classification model based on quadraticdiscriminant analysis, a classification model based on a forest ofdecision trees, a classification model using a bagging of decisiontrees, a classification model using a logistic regression, aclassification model using the method of k nearest neighbors, aclassification model using a boosting of weak classifiers.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the disclosure herein willbecome apparent on reading a preferential embodiment of the disclosureherein, done with reference to the attached figures among which:

FIG. 1 represents in a schematic manner a method of supervised learningto train a method for detecting freezing conditions according to oneembodiment of the disclosure herein;

FIG. 2 illustrates the performance of a plurality of models ofclassification after supervised learning according to FIG. 1;

FIG. 3 represents in a schematic manner a method for detecting freezingconditions according to one embodiment of the disclosure herein, aftersupervised learning according to FIG. 1; and

FIGS. 4A-4D represent in a schematic manner examples of detection offreezing conditions by various classifiers.

DETAILED DESCRIPTION

An idea underlying the disclosure herein is to use the availableaircraft data, without developing and installing specific externalprobes/sensors and therefore without implanting probes/sensors on theskin of the aircraft, to detect the presence of freezing conditions andestimate, if relevant, their degree of severity. By specific sensors ismeant here sensors whose measurements are exclusively intended fordetecting presence of ice (for example a detector of ice crystals). Byavailable aircraft data is meant data of aircraft systems whoseoperation is not degraded by the formation of ice, stated otherwise thedata which are reliable in such a situation (for example the dataarising from an anemometric probe, at risk of being blocked by ice, arenot considered to be available data).

When an aircraft encounters freezing conditions, certain elements ofsystems, such as sensors or control surface actuators, have acharacteristic response, symptomatic of the presence of ice. Thesesymptoms can vary in number, in intensity, in frequency according to thetype of freezing conditions encountered (crystals of ice or supercooledwater for example) and their degree of severity (concentration of icecrystals). As a consequence, it is possible to select certain parameterswhich are symptomatic (of freezing conditions) from among the availabledata of the aircraft's systems and to deduce therefrom explanatoryparameters (also termed explanatory variables or “features”) whichexplain the presence of freezing conditions and if relevant theirseverity. These explanatory variables are used as input to one or aplurality of classifiers so as to determine whether or not ice ispresent (binary classification) or to appraise the degree of severity ofthe freezing conditions (classification with K modalities where K is thenumber of classes). The classification models are trained by supervisedlearning on the basis of available data acquired by specificinstrumentation during flights carried out under freezing conditions, asexplained further on.

FIG. 1 represents in a schematic manner a method of supervised learningfor a system for detecting freezing conditions according to oneembodiment of the disclosure herein.

Prior to the supervised learning, the available data obtained duringtrial flights of an aircraft under freezing conditions are collected at110. These data are measurements of parameters of systems of theaircraft which are unsusceptible to operate in degraded mode in thepresence of ice. Furthermore, during these flights, the trial aircraftis equipped with sensors dedicated to the direct detection of ice,termed test sensors.

Consequently one has, on the one hand, measurements of aircraftparameters and, on the other hand, a diagnosis as regards the presenceor the absence of ice, optionally supplemented with a measurement of thewater content (crystals and supercooled water).

Next, from among the measured parameters, a plurality M of parameterswhich are symptomatic of the presence of ice is selected at 120. Thesesymptomatic parameters will advantageously be chosen from among thoselisted in chapters ATA 21 (air conditioning and pressurization), ATA 27(flight controls), ATA 28 (fuel), ATA 30 (ice and rain protection), ATA32 (landing gear), ATA 34 (navigation), ATA 36 (pneumatics), ATA 70 toATA 79 (engines, engine controls and indications, FADEC (Full AuthorityDigital Engine Control) channels). The symptomatic parameters selectedare typically temperatures, currents of heating circuits, pressures,disparities between actuator commands and feedbacks, kinematic(accelerations, rotation rate, speed), altimetric (altitude), barometric(barometric pressure) and anemometric (apparent wind speed) parameters.

By way of example, it is possible to choose in chapter ATA 21 theparameters related to the temperatures at various points of the cabin,to the temperatures of the ducts of the pressurization systems and tothe deicing controls, in chapter ATA 27 the parameters related to theaccelerations, to the clinometry, to the control of the surfaces(elevator and/or ailerons and/or spoiler), in chapter ATA 28 theparameters related to the fuel temperatures in each compartment, inchapter ATA 30 the parameters related to energy consumption and to theelectrical power supply of the components for deicing and protectionagainst the wind, in chapter ATA 32 the parameters related to thetemperatures of the landing gear, in ATA 34 the parameters related tothe attitude of the craft (pitch, roll, yaw), to the dynamicmeasurements (acceleration, rotation rate), to the anemobarometricmeasurements, in chapter ATA 36 the parameters related to the coolingsystem, and in chapter ATA 7X the parameters related to the vibrationsand/or to the engine regulation and control information.

According to the disclosure herein, the symptomatic parameters are notlimited to the ATA chapters listed hereinabove and may arise from otherchapters such as chapter ATA 42 (Integrated Modular Avionics).

The measurements of symptomatic parameters acquired at a given instantform a sample. The set of samples acquired during a measurement campaignis denoted S.

The symptomatic parameters measured are thereafter transformed intoexplanatory variables which explain the freezing conditions (operationdubbed “features extraction”) at 130. The transformation making itpossible to pass from the symptomatic parameters to the explanatoryvariables can notably comprise a calculation of a mean, of a median, ofa standard deviation, of a variance, a Fourier transform, a low-pass orhigh-pass filtering, a wavelet decomposition, a spectral densitycalculation, etc. The object of this operation is to delete or to reducethe non-explanatory information in the measurements and to preventover-learning (overfitting) on the symptomatic parameters measuredduring the trials. Hereinafter the explanatory variables are denoted X¹,. . . , X^(P). With each sample of S is thus associated a P-tuple ofvalues of explanatory variables. The freezing conditions, for theirpart, can be simply represented by a variable to be explained (or targetvariable) Y. This target variable is binary, when dealing with simplypredicting the presence or the absence of ice, or has K modalities, whendealing with predicting the degree of severity of the freezingconditions (K then being the number of degrees of severity).

The measurements of the test sensors are acquired in parallel at 140.These test sensors are for example Lyman-alpha hygrometric sensorscapable of giving the total water content or TWC, independently of thenature of its phase (liquid or vapor).

The measurements of the test sensors may be optionally supplemented at150 with contextual meteorological information originating from exteriorsources. On the basis of the measurements of the test sensors and, ifrelevant of this contextual meteorological information, the presence orotherwise of ice is determined at 160. Thus, a class (class labelling)can be allocated to each P-tuple of values of explanatory variables (andtherefore to each sample of S) at 130. The classification may be simplybinary (absence or presence of ice) or have K modalities, for examplethe following classification with 4 modalities:

-   -   absence of freezing condition (TWC≤0.5)    -   weak freezing condition (0.5<TWC≤1.5)    -   moderate freezing condition (1.5<TWC≤3)    -   severe freezing condition (TWC>3)

Other classes could be envisaged by the person skilled in the artwithout, however, departing from the framework of the disclosure herein.For example, a classification operating a distinction between therelative amount of crystals and the relative amount of supercooled watermay be envisaged.

On the basis of the P-tuples of explanatory variables and of the classeswhich are allocated to them, several classification models, F₁, . . . ,

can be trained on the set S, as indicated at 170. A classification modelis a function F associating with any P-tuple (x¹, x², . . . , x^(P)) ofvalues of explanatory variables a prediction {circumflex over (γ)} ofthe value of the variable to be explained Y. More precisely, thetraining of a classifier consists in or comprises defining, in the spaceof explanatory variables, the domains associated with each of thepossible modalities of the variable to be explained.

Various classification models can be envisaged, certain examples thereofbeing provided hereinafter:

Firstly, it will be possible to use a model of decision tree type suchas CART (Classification And Regression Tree). A classification bydecision tree is carried out by partitioning by dichotomy the space ofexplanatory variables according to a tree-like structure, a class beingassociated with each leaf of the decision tree. This classificationmodel is trained on a part T of the set S (training data set) and testedon the remaining part V of this set (validation data set).

Alternatively, one and the same classification model (for example, adecision tree) can be trained on subsets T₁, T₂, . . . , T_(N) of Swhich are obtained by subsampling S in a random manner. The Nclassifiers resulting from this training can be aggregated with the aidof an aggregation function (for example majority vote). This techniqueis known in supervised learning by the name bagging (or bootstrapaggregating).

According to a variant, a classification model of the type with a forestof decision trees (Random Forest Classifier) can also be used. Accordingto this approach, elementary decision-tree classifiers are trained onsubsets of S, each classifier using only part of the variables to beexplained. The elementary classifiers thus obtained are thereafteraggregated by a majority-vote decision, the predicted class being theone that garners the majority of the votes of the elementaryclassifiers.

Alternatively, a so-called boosting technique combining predictions ofseveral weak classifiers can also be used. A classifier is termed weakif its prediction error rate is slightly better than that of a purelyrandom prediction (random guessing). By combining the successivepredictions of these weak classifiers, a classifier exhibiting a lowerror rate (high accuracy level) can be obtained. The weak classifiersmay be for example decision-tree classifiers. There exist various typesof boosting depending on whether the weak classifier is trained on thesamples corresponding to the largest prediction errors of the precedingweak classifier (Adaboost) or on the square prediction errors of thisclassifier (Gradient Boosting).

The classification model can further be based on a linear discriminantanalysis or LDA or indeed a quadratic discriminant analysis or QDA.Linear discriminant analysis assumes that the covariance matrix of theexplanatory variables is identical for the various classes. The decisionboundaries in the space of the variables are then hyperplanes. When thecovariance matrices in the various classes are not identical, thedecision function has a quadratic form (QDA): it is possible to get backto the previous case by considering a space of larger dimensionrepresenting not only the explanatory variables themselves but alsoquadratic variables (pairwise products and squares of the explanatoryvariables).

Alternatively again, the classification model will be able to use aclassification according to the method of the k nearest neighbors ork-NN (k Nearest Neighbors). In this method, to predict the classassociated with a given P-tuple Ω of values of explanatory variables,there is undertaken the search for the P-tuples, ω₁, . . . , ω_(k) whichare nearest to Ω, that were obtained during the learning. The class ofthe P-tuple is then predicted as being the predominant class (majorityvote) from among the classes respectively associated with ω₁, . . . ,ω_(k).

Finally, a classification model based on a logistic regression(multinomial logistic regression in the case of a variable to beexplained with K modalities) may alternatively be used. According tothis approach, the a posteriori probabilities of the various classes,knowing a P-tuple of values of explanatory variables, are modelled bylinear functions. The coefficients of these functions can be determinedas those maximizing the logarithmic likelihood over the training set,the search for the maximum being performed in an iterative manner on thevalues of the coefficients.

Of course, yet other types of classifiers may be envisaged such as forexample state vector machines.

A description of the various classification models mentioned hereinabovemay be found in the work by T. Hastie et al. entitled “The elements ofstatistical learning”, 2^(nd) edition, 2017, published by Springer.

The performance of the

classifiers, F₁, . . . ,

, corresponding to the various classification models can thereafter becompared using a cross validation, as indicated at 180. According tothis approach, the set S of samples is partitioned into subsets (orbatches) S_(γ), γ=1, . . . , Γ, each classifier F_(q) being trained on abatch of samples

$\bigcup\limits_{\underset{\gamma \neq \lambda}{{\gamma = 1},\ldots,\Gamma}}S_{\gamma}$and its performance evaluated on the remaining subset S_(λ), doing sofor λϵ{1, . . . , Γ}. The performance of a classifier can be evaluatedin terms of mean of the absolute value or of the prediction error or ofmean square error over each subset, the best performing classifierleading to the lowest mean error. Alternatively, the performance of aclassifier can be evaluated as mean success rate of classification overeach subset.

The best performing classifier or classifiers on termination of thesupervised learning phase can thereafter be retained, as indicated at190.

The classifiers thus selected will thereafter be used in the icingconditions prediction phase as explained further on.

FIG. 2 represents the performance of a plurality of classificationmodels on termination of a supervised learning according to FIG. 1.

The various types of classification models are indicated along theabscissa, namely:

-   -   TREE is a decision-tree classification model;    -   QDA is a classification model using a quadratic discriminant        analysis;    -   LDA is a classification model using a linear discriminant        analysis;    -   RF is a classification model using a forest of decision trees;    -   BAGG is a classification model using a bagging of decision        trees;    -   LR is a classification model using a logistic regression;    -   KNN is a classification model using the method of the k nearest        neighbors;    -   BOOST is a classification model using a boosting of weak        classifiers.

In the figure, the success rate (accuracy) of each classifier has beenindicated along the ordinate. More precisely, for each classifier, thedistribution of the success rate has been represented by virtue of abox-and-whiskers plot (or simply boxplot). The distribution of thesuccess rate relates to the various partitions, used in the crossvalidation, of the set of samples. The whiskers correspond to theminimum value and to the maximum value of the success rate, the lowerand upper ends of a box correspond respectively to the lower quartileand to the upper quartile, the horizontal bar inside the box correspondsto the median value.

Advantageously, a classifier exhibiting a high success rate with a highmedian value is chosen, for example, the LR model and/or the BOOSTmodel.

FIG. 3 represents in a schematic manner a method for detecting freezingconditions according to one embodiment of the disclosure herein, aftersupervised learning according to FIG. 1.

The method of detection is implemented in the course of an operationalflight of an aircraft, generally of the same type as that used for thetrial flights except that this time it does not comprise any testsensors (ice detector) capable of directly indicating the presence orthe absence of ice.

In step 310, the available data of the systems of the aircraft arecollected at regular intervals, these systems being unsusceptible todegraded operation in the presence of ice. Stated otherwise, amodification of behaviour or change of state of these systems in thepresence of ice makes it possible to confirm the presence thereof, butwithout impairing flight safety.

In step 320, the measurements of the parameters which are symptomatic ofthe presence of ice are extracted and, if relevant, stored in a memory.These symptomatic parameters are in principle the same as those chosenfor the learning method. Stated otherwise, these symptomatic parameterswill have been chosen from among those listed in chapters ATA21, ATA27,ATA28, ATA30, ATA32, ATA34, ATA36, ATA70 to ATA79. However, if theclassifiers retained on termination of the learning period do not usecertain symptomatic parameters, the latter may be omitted in thisacquisition phase.

In step 330, the measurements of the symptomatic parameters into valuesof explanatory variables are transformed, as explained previously inconjunction with step 130 of FIG. 1.

The transformation of the symptomatic parameters is carried out by acalculation module, such as a processor configured for this purpose.

In step 370, each classifier, trained on the data of the trial flightsand selected in step 190 of the supervised learning predicts the classof icing conditions which is associated with the values of explanatoryvariables obtained in the previous step. The classification is of thesame type as that trained during the learning phase. It can be binary orlog₂ K-ary depending on whether a prediction of presence/absence of iceor a prediction of the degree of severity of the icing conditions isdesired.

In any event, when several classifiers have been selected, theirrespective predictions are consolidated in step 380, for exampleaccording to a majority vote procedure. When the number of selectedclassifiers is even, it may be agreed that one of them has a castingvote. According to a variant, regressors can be used instead of theclassifiers so as to each estimate a (continuous) degree of severity,and perform a mean between them before optional discretization.

According to the result of the consolidation, it is determined at 390whether or not ice is present (binary classification) or the degree ofseverity of the icing conditions (multinomial classification).

The classification, consolidation and prediction steps are performed byone or more calculation modules. These calculation modules can behardware modules or software modules, for example software modulesexecuted by the aforementioned processor. If relevant, the classifierscan be implemented in distinct processors operating in parallel,consolidation and prediction being performed by a programmablecombinatorial logic circuit, such as an FPGA. The person skilled in theart will be able to envisage various modes of implementation of thesesteps without departing from the scope of the disclosure herein.

The method for predicting icing conditions can be executed entirely onboard the aircraft, in an embedded item of equipment of FWC (FlightWarning Computer) or EFB (Electronic Flight Bag) type, after theclassifiers have been trained on the ground (or in the trial airplane).Alternatively, the symptomatic parameters can be transmitted to theground for remote monitoring of the ARTHM (Airbus Real Time HealthMonitoring) type with the prediction result being returned to theaircraft. In all cases, the predicted or estimated icing condition maybe displayed on a screen of the cockpit and optionally generate analarm. The pilot will then have the possibility of activating theanti-ice protection systems. Alternatively, the icing condition maytrigger anti-ice protection systems automatically.

By way of example, a method for detecting icing conditions is describedhereinafter.

The symptomatic parameters have been chosen in ATA27, ATA34 and ATA7Xnamely the redundant flight control parameters FCPC (Flight ControlPrimary Computer)*_FCPC1_COM; *_FCPC2_COM; *_FCPC3_COM, the redundantkinematic parameters ADIRU (Air Data Inertial Reference Unit) ADIRU_*_1,ADIRU_*_2, ADIRU_*_3 and the regulation channels A-B FADEC of the twoengines, namely POLOCAL_[1;2]A; POLOCAL_[1;2]B; T12LOCAL_[1;2]A;T12LOCAL_[1;2]B.

The explanatory variables are obtained by taking:

-   -   the median value of *_FCPC1_COM, *_FCPC2_COM, *_FCPC3_COM and        then by calculating the min, max, mode and median value of the        value obtained over a sliding window of 10 s,    -   the median value of ADIRU_*_1, ADIRU_*_2, ADIRU_*_3 and then by        calculating the min, max, mode and median value of the value        obtained over a sliding window of 10 s,    -   the maximum value of POLOCAL_[1;2]A and POLOCAL_[1;2]B, and then        by calculating the min, max, mode and median value of the value        obtained over a sliding window of 10 s,    -   the maximum value of T12LOCAL_[1;2]A; T12LOCAL_[1;2]B, and then        by calculating the min, max, mode and median value of the value        obtained over a sliding window of 10 s.

The classification had 4 degrees of severity of icing conditions asindicated above.

However, instead of using a single multinomial classifier, 4 binaryclassifiers were used for each of the intervals of TWC. The 4classifiers are based on independent classification models of GradientBoosting type. Table I indicates the performance of the classifiers interms of success rate (accuracy) and precision (sensitivity):

TABLE I τ (%) σ (%) model #1 96.80 97.16 model #2 96.07 97.96 model #397.32 82.08 model #4 97.36 88.33

The success rate τ is defined as the ratio between the sum of the numberof predictions which are actually positive (TP) and of the number ofpredictions which are actually negative (TN) over the set of positiveand negative predictions (erroneous or not):

$\tau = \frac{{TP} + {TN}}{{TP} + {TN} + {FP} + {FN}}$where FP (resp, EN) is the number of falsely positive (falsely negative)predictions.

The precision is the fraction of positive predictions that are actuallypositive:

$\sigma = \frac{TP}{{TP} + {FP}}$

It is consequently possible to correctly classify the freezingconditions on the basis of symptomatic parameters without adding anyspecific probe (ice sensor) and with a success rate of the order of 80%.

FIGS. 4A through 4D represent the results of classifying freezingconditions by classifiers based on the aforementioned fourclassification models.

The first classification model in FIG. 4A predicts the condition (binaryvariable to be explained) TWC≤0.5, the second classification model inFIG. 4B predicts the condition 0.5<TWC≤1.5, the third classificationmodel in FIG. 4C predicts the condition 1.5<TWC≤3 and finally the fourthclassification model in FIG. 4D predicts the condition TWC>3. For eachof these figures, the actual freezing condition has been represented inthe upper part, and the freezing condition predicted by thecorresponding classifier has been represented in the lower part. Theperson skilled in the art will note a very good correlation between thepredicted conditions and the actual conditions whatever the degree ofseverity of the icing conditions.

The subject matter disclosed herein can be implemented in software incombination with hardware and/or firmware. For example, the subjectmatter described herein can be implemented in software executed by aprocessor or processing unit. In one exemplary implementation, thesubject matter described herein can be implemented using a computerreadable medium having stored thereon computer executable instructionsthat when executed by a processor of a computer control the computer toperform steps. Exemplary computer readable mediums suitable forimplementing the subject matter described herein include non-transitorydevices, such as disk memory devices, chip memory devices, programmablelogic devices, and application specific integrated circuits. Inaddition, a computer readable medium that implements the subject matterdescribed herein can be located on a single device or computing platformor can be distributed across multiple devices or computing platforms.

While at least one exemplary embodiment of the invention(s) is disclosedherein, it should be understood that modifications, substitutions andalternatives may be apparent to one of ordinary skill in the art and canbe made without departing from the scope of this disclosure. Thisdisclosure is intended to cover any adaptations or variations of theexemplary embodiment(s). In addition, in this disclosure, the terms“comprise” or “comprising” do not exclude other elements or steps, theterms “a”, “an” or “one” do not exclude a plural number, and the term“or” means either or both. Furthermore, characteristics or steps whichhave been described may also be used in combination with othercharacteristics or steps and in any order unless the disclosure orcontext suggests otherwise. This disclosure hereby incorporates byreference the complete disclosure of any patent or application fromwhich it claims benefit or priority.

The invention claimed is:
 1. A method for detecting icing conditions foran aircraft, the method comprising: measuring parameters of systems ofthe aircraft with exception of ice-detecting external probes, thesystems being unsusceptible to degraded operation in presence of ice andthe parameters being symptomatic of the presence of ice on the aircraft;transforming measurements of the measured parameters into P-tuples ofvalues of explanatory variables which explain the icing conditions; andclassifying the measurements by at least one classifier previouslytrained in a supervised manner, the classifier providing a prediction ofmembership in a class of icing conditions; wherein the parameters of thesystems of the aircraft comprise parameters from one or more of ATA21,ATA27, ATA28, ATA30, ATA32, ATA34, ATA36, and ATA70 to ATA79.
 2. Themethod for detecting icing conditions according to claim 1, wherein theparameters comprise one or more of temperatures, currents of heatingcircuits, pressures, disparities between actuator commands andfeedbacks, and kinematic, altimetric, barometric, and anemometricparameters.
 3. The method for detecting icing conditions according toclaim 1, wherein the measurements of the measured parameters aretransformed into values of explanatory variables by calculating a mean,a median, a standard deviation, a variance, a Fourier transform, alow-pass or high-pass filtering, a wavelet decomposition, or a spectraldensity calculation.
 4. The method for detecting icing conditionsaccording to claim 1, wherein the classifying is performed by aplurality of classifiers, respective predictions of the classifiersbeing consolidated, a result of the consolidation giving a prediction ofpresence or absence of ice or otherwise, or else a degree of severity oficing conditions.
 5. The method for detecting icing conditions accordingto claim 4, wherein the classifiers use classification models selectedfrom the group consisting of a decision-tree classification model, aclassification model based on linear discriminant analysis, aclassification model based on quadratic discriminant analysis, aclassification model based on a forest of decision trees, aclassification model using a bagging of decision trees, a classificationmodel using a logistic regression, a classification model using themethod of k nearest neighbors, and a classification model using aboosting of weak classifiers.
 6. The method for detecting icingconditions according to claim 4, wherein the measurements of parametersare transmitted by the aircraft to a ground station, the ground stationperforming the transforming and classifying and then returning a resultof the consolidation to the aircraft.
 7. A method of supervised trainingof a method for predicting icing conditions according to claim 1,comprising: measuring parameters of systems of the aircraft during aflight under freezing conditions; transforming measurements of themeasured parameters into P-tuples of values of explanatory variableswhich explain the icing conditions; detecting presence of freezingconditions during the flight by dedicated probes situated on theaircraft; allocating classes of freezing conditions to the measurementson a basis of the detected freezing conditions; training a plurality ofclassifiers on a basis of the explanatory variables and of correspondingclasses allocated; comparing prediction performance of the classifiersby cross-validation over the measurements; and selecting at least oneclassifier from among best performing classifiers to predict the icingconditions; wherein the parameters of the systems of the aircraftcomprise parameters from one or more of ATA21, ATA27, ATA28, ATA30,ATA32, ATA34, ATA36, and ATA70 to ATA79.
 8. The method of supervisedtraining according to claim 7, wherein detecting presence of freezingconditions during the flight also uses meteorological sources externalto the aircraft.
 9. The method of supervised training according to claim7, wherein the prediction performance of a classifier is estimated on abasis of a mean absolute value of prediction error or of a mean squarevalue of the prediction error or of a mean success rate of predictionover the measurements.
 10. The method of supervised training accordingto claim 9, wherein the classifiers use classification models selectedfrom the group consisting of a decision-tree classification model, aclassification model based on linear discriminant analysis, aclassification model based on quadratic discriminant analysis, aclassification model based on a forest of decision trees, aclassification model using a bagging of decision trees, a classificationmodel using a logistic regression, a classification model using themethod of k nearest neighbors, and a classification model using aboosting of weak classifiers.